Spectral Hadamard microscopy with metasurface-based patterned illumination.

Hadamard matrices, composed of mutually orthogonal vectors, are widely used in various applications due to their orthogonality. In optical imaging, Hadamard microscopy has been applied to achieve optical sectioning by separating scattering and background noise from desired signals. This method involves sequential illumination using Hadamard patterns and subsequent image processing. However, it typically requires costly light modulation devices, such as digital micromirror devices (DMDs) or spatial light modulators (SLMs), to generate multiple illumination patterns. In this study, we present spectral Hadamard microscopy based on a holographic matasurface. We noticed that certain patterns repeat within other Hadamard patterns under specific condition, allowing the entire set to be reproduced from a single pattern. This finding suggests that generating a single pattern is sufficient to implement Hadamard microscopy. To demonstrate this, we designed a metasurface to generate an illumination pattern and conducted imaging simulations. Results showed that holographic metasurface-based Hadamard microscopy effectively suppressed scattering signals, resulting in clear fluorescent images. Furthermore, we demonstrated that hyperspectral imaging can be achieved with Hadamard microscopy using dispersive optical elements, as the orthogonality of the Hadamard pattern enables to resolve spectral information. The reconstructed hyperspectral images displayed a color distribution closely matching the synthetic hyperspectral images used as ground truth. Our findings suggest that optical sectioning and hyperspectral imaging can be accomplished without light modulation devices, a capability typically unattainable with standard wide-field microscopes. We showed that sophisticated metasurfaces have the potential to replace and enhance conventional optical components, and we anticipate that this study will contribute to advancements in metasurface-based optical microscopy.